MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  necon1biOLD Structured version   Unicode version

Theorem necon1biOLD 2701
Description: Obsolete proof of necon1bi 2700 as of 22-Nov-2019. (Contributed by NM, 18-Mar-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
necon1bi.1  |-  ( A  =/=  B  ->  ph )
Assertion
Ref Expression
necon1biOLD  |-  ( -. 
ph  ->  A  =  B )

Proof of Theorem necon1biOLD
StepHypRef Expression
1 necon1bi.1 . . 3  |-  ( A  =/=  B  ->  ph )
21con3i 135 . 2  |-  ( -. 
ph  ->  -.  A  =/=  B )
3 nne 2668 . 2  |-  ( -.  A  =/=  B  <->  A  =  B )
42, 3sylib 196 1  |-  ( -. 
ph  ->  A  =  B )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1379    =/= wne 2662
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-ne 2664
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator